This sounds like it might be a problem with Lightroom rather than with the Juicebox plugin.
The resizing and exporting of images is handled by Lightroom itself.
Does this happen when you try to create a gallery with the same images using a different Web Engine (something other than Juicebox) but exporting at the same image size?
What version of Lightroom are you using and how much RAM does your computer have?
Try creating a test gallery with fewer images to see if this makes a difference.
Also, check that you are not exporting your gallery to a restricted (read-only) folder or to a network drive.
Try exporting to a folder on your desktop to see if this helps.